Tag: transfer of heat

Questions Related to transfer of heat

Two thin walled sphere of different materials ,one with double the radius and one fourth wall thickness of the other are filled with ice If the time taken for complete melting of ice in the sphere of larger radius is $25$ minutes and that for smaller one is $16$ minutes,the ratio of thermal conductivities of the materials of larger sphere to the smaller sphere is  

  1. $4:5$

  2. $25:1$

  3. $1:25$

  4. $8:25$


Correct Option: D

Iron, lead and brass spheres of equal masses are heated to a common temperature and are kept on a sheet of wax. The sphere that passes through the plate first is (lead 0.03 $\operatorname { cal } / \mathrm { g } / ^ { \circ } \mathrm { C }$, iron 0.11 $\operatorname { cal } / \mathrm { g } / ^ { \circ } \mathrm { C }$, brass 0.08 $\operatorname { cal } / \mathrm { g } / ^ { \circ } \mathrm { C }$) 

  1. lead

  2. brass

  3. iron

  4. all at the same time


Correct Option: D

Glaciers melt:

  1. first at the bootom due to decress in pressure

  2. first at the top due to iuncrease in pressure

  3. first at the bottom due to increase in pressure

  4. first at the top due to increase in pressure


Correct Option: C

Two rods having thermal conductivities in the ratio of 5:3 and having equal length length and equal cross-section are joined by face to face. If the temperature of free end of first rod is $100^oC$ and temperature of  free end of second rod is $20^oc$, then temperature of the junction, is-

  1. $90^oC$

  2. $85^oC$

  3. $70^oC$

  4. $50^oC$


Correct Option: C
Explanation:

Let the thermal conductivity of first rod be $5 K$

Let the thermal conductivity of second rod be $3 k$
now, sum of heat current flowing through the junction =0
$\begin{array}{l} \frac { { 5KA\left( { 100-T } \right)  } }{ x } +\frac { { 3KA\left( { 20-T } \right)  } }{ x } =0 \ 500-5T+60-3T=0 \ 8T=560 \ \therefore T={ 70^{ 0 } }C \end{array}$

Select and write the most appropriate answer from the given aternative in question:
Which of the following substances is ductile?

  1. Glass

  2. High carbon steel

  3. Steel

  4. Copper


Correct Option: C

Two walls of thickness $d _1$ and $d _2$, thermal conductivities $K _1$ and $K _2$ are in contact. In the steady state if the temperatures at the outer surfaces are $T _1$ and $T _2$, the temperature at the common wall will be

  1. $\dfrac{K _1T _1+K _2T _2}{d _1+d _2}$

  2. $\dfrac{K _1T _1d _2+K _2T _2d _1}{K _1d _2+K _2d _1}$

  3. $\dfrac{(K _1d _1+K _2d _2)T _1T _2}{T _1+T _2}$

  4. $\dfrac{K _1d _1T _1+K _2d _2T _2}{K _1d _1+K _2d _2}$


Correct Option: B

$\triangle { H }^{ \circ  }$ for reaction: 
${ F } _{ 2 }+2HCI\rightarrow 2HF+{ CI } _{ 2 }$
is equal to -352.8kJ. If $\triangle { H } _{ f }^{ \circ  }$ for HF is -268.3 kJ ${ mol }^{ -1 }$ then ${ \triangle H } _{ f }^{ \circ  }$ of HCI would be:- 

  1. -22 kJ ${ mol }^{ -1 }$

  2. 88.0 kJ ${ mol }^{ -1 }$

  3. 01.0 kJ${ mol }^{ -1 }$

  4. None


Correct Option: C

A hetaed smooth metallic body is allowed to cool in air. Which of the following statements about its heat loss is incorrect?

  1. Convection currents in the air aid the process of heat loss.

  2. Conduction is the main mode of heta loss as the body is a good conductor of heat

  3. The rate of heat loss by thermal radiation is increased due to its metallic surface.

  4. The rate of heat loss decreases as the temperature of teh body nears room temperature


Correct Option: C

Spheres $P$ and $Q$ are uniformly constructed from the same material which is a good conductor of heat and the radius of $Q$is thrice the radius of $P$. The rate of fall of temperature of $P$ is $x$ times that of $Q$ when both are at the same surface temperature. The value of $x$ is:

  1. $1/4$

  2. $1/3$

  3. $3$

  4. $4$


Correct Option: C

If we convert a sphere of radius $'r'$ into a cylinder of radius $r$ at same temperature the rate of heat loss will  becomes if both are placed at same surrounding-

  1. $7/6$

  2. $6/7$

  3. $4/3$

  4. remain same


Correct Option: A